SOLUTION: A car starts from town A towards town B. Another car starts from town B towards town A at the same time. The pass each other 64km from town B. Both cars continued on their journ
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Question 446506: A car starts from town A towards town B. Another car starts from town B towards town A at the same time. The pass each other 64km from town B. Both cars continued on their journey after passing each other. When they reach the respective towns, they turn around, back to where they came from. This time, they pass each other 52km from town A. What is the distance between town A & B? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A car starts from town A towards town B.
Another car starts from town B towards town A at the same time.
The pass each other 64km from town B. Both cars continued on their journey after passing each other.
When they reach the respective towns, they turn around, back to where they came from.
This time, they pass each other 52km from town A. What is the distance between town A & B?
:
A rough diagram of this (first meeting):
:
Let d = distance from a to b
:
A --------------------d-----------------------B
car a>--------(d-64)------*-----64------< car b
:
First time they meet:
car a travels (d-64) km
car b travels 64 km
:
2nd meeting
car b>----52-------*--------(d-52)------< car a
:
car a travels 64 + (d-52) = (d+12)
car b travels (d-64) + 52 = (d-12)
:
The ratio a:b of the distances traveled by the two cars remain the same; therefore:
1st meeting = 2nd meeting =
;
Cross multiply
(d-64)(d-12) = 64(d+12)
d^2 - 12d - 64d + 768 = 64d + 768
;
Subtract 768 from both sides, arrange as a quadratic equation
d^2 - 76d - 64d = 0
d^2 - 140d = 0
;
Factor
d(d - 140) = 0
;
Two solutions
d = 0
and
d = 140 km distance between the towns
:
:
Find a way to check this:
First meeting:
a travels (140-64) = 76 mi
b travels 64 mi
Second meeting
a travels 64 + (140-52) = 152 mi
b travels (140-64) + 52 = 128 mi
;
Check the ratios
76/64 = 1.1875
152/128 = 1.1875; confirms our distance of 140 km
